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Recent developments have made it possible to construct materials that behave in the millimeter and higher frequency regimes as if they have negative relative permittivity and permeability. As a result exotic-seeming wave-propagation properties that have been largely ignored since first predicted have become interesting. We review a recent claim that the initial decay in amplitude of evanescent plane-wave components of a signal in free space can be restored upon entry into an ε<0, μ<0 double negative (DNG) medium. We find, in a case study of a DNG medium with realizable parameters, that there is a minimal slab width d beyond which the field amplitude of any signal with nonzero bandwidth will decay with increasing d.